Questions: Exhibit 1: Use the following for the next 4 questions, 30% of the acc

Question

Questions: Exhibit 1: Use the following for the next 4 questions, 30% of the accidents in a highway occur in the morning. A random sample of ten (n-10) accidents will be taken. Let X be the total number of accidents in the sample that take place in the morning. Answer the following questions using the Binomial distribution 5. Refer to Exhibit 1. What is the probability that exactly 5 accidents occur in the morning? Le P(X = 5) 10 points/5 min.] 6. Refer to Exhibit 1. What is the probability that less than 2 accidents occur in the moning? i.e. P(X

Explanation / Answer

We have X ~ Binom(10,0.3).

5. P(X = 5) = 10C5 * 0.35 * (1 - 0.3)5

= 252 * 0.35 * 0.75

= 0.1029.

6. P(X < 2) = P(X = 0) + P(X = 1)

P(X = 0) = (1 - 0.3)10 = 0.710

P(X = 1) = 10 * 0.3 * 0.79 = 3 * 0.79

=> P(X < 2) = 0.710 + 3 * 0.79 = 0.1493.

7. Expected number of accidents that do not occur

= n * (1 - p)

= 10 * (1 - 0.3)

= 10 * 0.7

= 7.

8. Standard deviation of the number of accidents that occur

= (np(1-p))

= (10*0.3*(1-0.3))

= (3*0.7)

= 2.1

= 1.4491.

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